If non-humans are not speaking English then why are their mouths forming English words?

Kind of goes back to my watching Star Trek in Spanish (which perhaps I should have expanded on), I'm use to the spoken words heard being different than the lip motions observed.

It would be the same with an conversation where the UT is in use.

Also acoustically you would hear Bajora being spoken from the Bajorans and FS coming from the UT. That could get distracting pretty quick...

There is a scene in DS9 where Sisko in his role as the emissary renders a blessing over a engaged/newly wed Bajor couple. He does this speaking the Bajorian language, this is specifically commented upon in the episode with Kira complimenting Sisko on his accent.

When Kira is talking to one of her fellow Bajorians, she is most likely speaking a Bajorian language, say during one of her conversations with Kai Winn.

Personally, I believe whole segments of the dialog in Amok Time is in Vulcan.

When Worf is aboard a Klingon ship, surround (so to speak) by other Klingons, he is speaking a Klingon dialect. Worf likely does speak either English or "Starfleet standard." And when speaking with his adopted family in private, the conversation could easily be in Ukrainian.